Off-diagonal disorder in the Anderson model of localization

We examine the localization properties of the Anderson Hamiltonian with additional off-diagonal disorder using the transfer-matrix method and finite-size scaling. We compute the localization lengths and study the metal-insulator transition (MIT) as a function of diagonal disorder, as well as its energy dependence. Furthermore we investigate the different influence of odd and even system sizes on the localization properties in quasi one-dimensional systems. Applying the finite-size scaling approach in conjunction with a nonlinear fitting procedure yields the critical parameters of the MIT. In three dimensions, we find that the resulting critical exponent of the localization length agrees with the exponent for the Anderson model with pure diagonal disorder.Comment: 12 pages including 4 EPS figures, accepted for publication in phys. stat. sol. (b

Glass phases of flux lattices in layered superconductors

We study a flux lattice which is parallel to superconducting layers, allowing for dislocations and for disorder of both short wavelength and long wavelength. We find that the long wavelength disorder has a significant effect on the phase diagram -- it produces a first order transition within the Bragg glass phase and leads to melting at strong disorder. This then allows a Friedel scenario of 2D superconductivity.Comment: 5 pages, 1 eps figure, Revte

Exciton states in monolayer MoSe2 and MoTe2 probed by upconversion spectroscopy

Transitions metal dichalcogenides (TMDs) are direct semiconductors in the atomic monolayer (ML) limit with fascinating optical and spin-valley properties. The strong optical absorption of up to 20 % for a single ML is governed by excitons, electron-hole pairs bound by Coulomb attraction. Excited exciton states in MoSe$_2$ and MoTe$_2$ monolayers have so far been elusive due to their low oscillator strength and strong inhomogeneous broadening. Here we show that encapsulation in hexagonal boron nitride results in emission line width of the A:1$s$ exciton below 1.5 meV and 3 meV in our MoSe$_2$ and MoTe$_2$ monolayer samples, respectively. This allows us to investigate the excited exciton states by photoluminescence upconversion spectroscopy for both monolayer materials. The excitation laser is tuned into resonance with the A:1$s$ transition and we observe emission of excited exciton states up to 200 meV above the laser energy. We demonstrate bias control of the efficiency of this non-linear optical process. At the origin of upconversion our model calculations suggest an exciton-exciton (Auger) scattering mechanism specific to TMD MLs involving an excited conduction band thus generating high energy excitons with small wave-vectors. The optical transitions are further investigated by white light reflectivity, photoluminescence excitation and resonant Raman scattering confirming their origin as excited excitonic states in monolayer thin semiconductors.Comment: 14 pages, 7 figures, main text and appendi

Representation of a complex Green function on a real basis: I. General Theory

When the Hamiltonian of a system is represented by a finite matrix, constructed from a discrete basis, the matrix representation of the resolvent covers only one branch. We show how all branches can be specified by the phase of a complex unit of time. This permits the Hamiltonian matrix to be constructed on a real basis; the only duty of the basis is to span the dynamical region of space, without regard for the particular asymptotic boundary conditions that pertain to the problem of interest.Comment: about 40 pages with 5 eps-figure

Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants

The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions, and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.Comment: 30 page

Origin of four-fold anisotropy in square lattices of circular ferromagnetic dots

We discuss the four-fold anisotropy of in-plane ferromagnetic resonance (FMR) field $H_r$, found in a square lattice of circular Permalloy dots when the interdot distance $a$ gets comparable to the dot diameter $d$. The minimum $H_r$, along the lattice $$axes, and the maximum, along the$$ axes, differ by $\sim$ 50 Oe at $a/d$ = 1.1. This anisotropy, not expected in uniformly magnetized dots, is explained by a non-uniform magnetization \bm(\br) in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variational procedure.Comment: 4 pages, 3 figures, revtex, details of analytic calculation and new references are adde

Relaxation of Spin Polarized 3^3He in Mixtures of 3^3He and 4^4He Below the 4^4He Lambda Point

We report the first study of the depolarization behavior of spin polarized 3He in a mixture of 3He-4He at a temperature below the 4He Lambda point in a deuterated TetraPhenyl Butadiene-doped deuterated PolyStyrene (dTPB-dPS) coated acrylic cell. In our experiment the measured 3He relaxation time is due to the convolution of the 3He longitudinal relaxation time, T1, and the diffusion time constant of 3He in superfluid 4He since depolarization takes place on the walls. We have obtained a 3He relaxation time ~3000 seconds at a temperature around 1.9K. We have shown that it's possible to achieve values of wall depolarization probability on the order of (1-2)x10^-7 for polarized 3He in the superfluid 4He from a dTPB-dPS coated acrylic surface.Comment: The Model used to interpret the data has been change

Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects

The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond--Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.Comment: 24 pages, 3 figures, previously known as "A User Manual for the Fisher Information Matrix"; final, corrected PRD versio